Advanced Search

Question: integro-differential equation

Question:integro-differential equation

mehdi jafari 769 Maple
ode dsolve numeric differential-equations integro-differential-equation
November 07 2024
1

how this integro-differential equation can be solved?
any assumption or suggestion is appreciated. tnx in advance

> 

restart
> 

eq:=diff(y(x),x)=y(x)+exp(x)*exp(-3*x)/2+int(exp(x+t)*y(t),t=0..x);
> 

IC:=y(0)=1;

diff(y(x), x) = y(x)+(1/2)*exp(x)*exp(-3*x)+int(exp(x+t)*y(t), t = 0 .. x)

  

y(0) = 1

 (1)
> 

eq2:=g(x)=int(exp(x+t)*y(t),t=0..x);

g(x) = int(exp(x+t)*y(t), t = 0 .. x)

 (2)
> 

IC_2:=eval(eq2,[x=0,y=1])

g(0) = 0

 (3)
> 

sys:={diff(eq2,x),subs(rhs(eq2)=lhs(eq2),eq)}

{diff(g(x), x) = int(exp(x+t)*y(t), t = 0 .. x)+exp(2*x)*y(x), diff(y(x), x) = y(x)+(1/2)*exp(x)*exp(-3*x)+g(x)}

 (4)
> 

dsolve(sys union {IC,IC_2},numeric)

Error, (in dsolve/numeric/process_input) input system must be an ODE system, got independent variables {t, x}

  

Download integro-diffrential_problem.mw
Please Wait...